From ab initio to continuum: Linking multiple scales using deep-learned forces.

We develop a deep learning-based algorithm, called DeepForce, to link ab initio physics with the continuum theory to predict concentration profiles of confined water. We show that the deep-learned forces can be used to predict the structural properties of water confined in a nanochannel with quantum scale accuracy by solving the continuum theory given by Nernst-Planck equation. The DeepForce model has an excellent predictive performance with a relative error less than 7.6% not only for confined water in small channel systems (L < 6 nm) but also for confined water in large channel systems (L = 20 nm) which are computationally inaccessible through the high accuracy ab initio molecular dynamics simulations. Finally, we note that classical Molecular dynamics simulations can be inaccurate in capturing the interfacial physics of water in confinement (L < 4.0 nm) when quantum scale physics are neglected.

Phonon-Fluid Coupling Enhanced Water Desalination in Flexible Two-Dimensional Porous Membranes.

Water purification using 2D nanoporous membranes has been drawing significant attention for over a decade because of fast water transport in ultrathin membranes. We perform a comprehensive study using molecular dynamics (MD) simulations on water desalination using 2D flexible membranes where the coupling between the fluid dynamics and mechanics of the membrane plays an important role. We observe that a considerable deformation and fluctuation in the 2D membrane results in an enhanced water permeability (up to 122%) along with a slight decrease in the salt rejection rate (less than 11%). Simulations on harmonically vibrating membranes indicate that the vibrational match at the membrane-water interface can significantly increase the permeance. We conduct mechanical stability tests and discuss the maximum endurable pressure of 2D porous membranes for water desalination. These findings will contribute to advances in applications using ultrathin membranes, such as energy harvesting and molecular separation.

Multi-scale simulation of proton diffusion in dislocation cores in BaZrO3.

Dislocations are important for their effects on the chemical, electrical, magnetic, and transport properties of oxide materials, especially for electrochemical devices such as solid fuel cells and resistive memories, but these effects are still under-studied at the atomic level. We have developed a quantum mechanical/molecular mechanical (QM/MM)-based multiscale simulation program to reveal the diffusion properties of protons on 〈100〉 edge dislocations in BaZrO3 perovskite oxide. We find that the large free space and the presence of hydrogen bonds in the dislocation core structure lead to significant trapping of protons. The diffusion properties of protons in dislocation cores were investigated, and no evidence of pipeline diffusion was found from the calculated migration energy barriers, which not only did not accelerate ion diffusion but rather decreases the conductivity of ions. The proton diffusion properties of Y-doped BaZrO3 (BZY), with a dislocation core structure (BZY-D) and with a grain boundary structure (BZY-GB) were also compared. In all three structures, local lattice deformation occupies an essential part in the proton transfer and rotation processes. The change in bond order is calculated and it is found that the interaction with oxygen and Zr ions during proton transfer and rotation controls the energy barrier for local lattice deformation of the O-B-O motion, which affects the proton diffusion in the structure. Our study provides insight into proton diffusion in dislocations in terms of mechanical behavior, elucidates the origin of the energy barrier associated with proton diffusion in dislocations, and provides guidance for the preparation and application of proton conductors.

Many-Body Neural Network-Based Force Field for Structure-Based Coarse-Graining of Water.

High-fidelity results from atomistic simulations can only be obtained by using accurate force-field (FF) parameters. Although empirical FFs are commonly used in the modeling of atomistic systems due to their simplicity, they have many limitations inherent in the crude approximations associated with their analytical form. Recent advances in neural network-based FFs have led to more accurate FFs by using symmetry functions or full many-body expansions. However, this approach leads to several issues including the arbitrariness of the symmetry functions, and the intangible and uninterpretable interactions which are only known once the positions of all atoms are set. More importantly, training is another bottleneck, as high-quality force and energy information is required, which is usually not accessible from experimental data. To solve these issues within the context of structure-based coarse-graining methods, we switch in this work to a local-search method to target the reference structure instead of using conventional backpropagation algorithms used to target the forces and energies of the reference structure. Our FF is decomposed into two-, three-, and higher-order terms, where each term is modeled with a separate neural network. To show the versatility of our method, we study four different systems, namely, Stillinger-Weber particles as an atomistic case and three water models, namely SPC/E, MB-pol, and ab initio, as coarse-graining cases. We show the successful application of our approach, by reproducing structural properties of different water models, followed by providing insight into the role of two-and three-body interactions. The results of all models indicate that the double-well isotropic pair potential, the signature of water-like behavior in an isotropic system, vanishes upon inclusion of the three-body interaction, showing dominance of the three-body interaction over the two-body interaction in water-like behavior with the single-well isotropic pair potential.

Extended DeepILST for Various Thermodynamic States and Applications in Coarse-Graining.

Molecular dynamics (MD) simulations are widely used to obtain the microscopic properties of atomistic systems when the interatomic potential or the coarse-grained potential is known. In many practical situations, however, it is necessary to predict the interatomic or coarse-grained potential, which is a tremendous challenge. Many approaches have been developed to predict the potential parameters based on various techniques, including the relative entropy method, integral equation theory, etc., but these methods lack transferability and are limited to a specific range of thermodynamic states. Recently, data-driven and machine learning approaches have been developed to overcome such limitations. In this study, we expand the range of thermodynamic states used to train deep inverse liquid-state theory (DeepILST)1, a deep learning framework for solving the inverse problem of liquid-state theory. We also assess the performance of DeepILST in coarse-graining various multiatom molecules and identify the molecular characteristics that affect the coarse-graining performance of DeepILST.

Nonlocal hydrodynamic model for gravity-driven transport in nanochannels.

It has been established that Newton's law of viscosity fails for fluids under strong confinement as the strain-rate varies significantly over molecular length-scales. We thereby investigate if a nonlocal shear stress accounting for the strain-rate of an adjoining region by a convolution relation with a nonlocal viscosity kernel can be employed to predict the gravity-driven isothermal flow of a Weeks-Chandler-Andersen fluid in a nanochannel. We estimate, using the local average density model, the fluid's viscosity kernel from isotropic bulk systems of corresponding state points by the sinusoidal transverse force method. A continuum model is proposed to solve the nonlocal hydrodynamics whose solutions capture the key features and agree qualitatively with the results of non-equilibrium molecular dynamics simulations, with deviations observed mostly near the fluid-channel interface.

Deep learning-based quasi-continuum theory for structure of confined fluids.

Predicting the structural properties of water and simple fluids confined in nanometer scale pores and channels is essential in, for example, energy storage and biomolecular systems. Classical continuum theories fail to accurately capture the interfacial structure of fluids. In this work, we develop a deep learning-based quasi-continuum theory (DL-QT) to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid and water confined in a nanochannel. The deep learning model is built based on a convolutional encoder-decoder network (CED) and is applied for high-dimensional surrogate modeling to relate the fluid properties to the fluid-fluid potential. The CED model is then combined with the interatomic potential-based continuum theory to determine the concentration profiles of a confined LJ fluid and confined water. We show that the DL-QT model exhibits robust predictive performance for a confined LJ fluid under various thermodynamic states and for water confined in a nanochannel of different widths. The DL-QT model seamlessly connects molecular physics at the nanoscale with continuum theory by using a deep learning model.

Understanding simple liquids through statistical and deep learning approaches.

Statistical and deep learning-based methods are employed to obtain insights into the quasi-universal properties of simple liquids. In the first part, a statistical model is employed to provide a probabilistic explanation for the similarity in the structure of simple liquids interacting with different pair potential forms, collectively known as simple liquids. The methodology works by sampling the radial distribution function and the number of interacting particles within the cutoff distance, and it produces the probability density function of the net force. We show that matching the probability distribution of the net force can be a direct route to parameterize simple liquid pair potentials with a similar structure, as the net force is the main component of the Newtonian equations of motion. The statistical model is assessed and validated against various cases. In the second part, we exploit DeepILST [A. Moradzadeh and N. R. Aluru, J. Phys. Chem. Lett. 10, 1242-1250 (2019)], a data-driven and deep-learning assisted framework to parameterize the standard 12-6 Lennard-Jones (LJ) pair potential, to find structurally equivalent/isomorphic LJ liquids that identify constant order parameter [τ=∫0 ξcf gξ-1ξ2dξ, where gξ and ξ(=rρ13) are the reduced radial distribution function and radial distance, respectively] systems in the space of non-dimensional temperature and density of the LJ liquids. We also investigate the consistency of DeepILST in reproducibility of radial distribution functions of various quasi-universal potentials, e.g., exponential, inverse-power-law, and Yukawa pair potentials, quantified based on the radial distribution functions and Kullback-Leibler errors. Our results provide insights into the quasi-universality of simple liquids using the statistical and deep learning methods.

Ultrathin, transferred layers of thermally grown silicon dioxide as biofluid barriers for biointegrated flexible electronic systems.

Materials that can serve as long-lived barriers to biofluids are essential to the development of any type of chronic electronic implant. Devices such as cardiac pacemakers and cochlear implants use bulk metal or ceramic packages as hermetic enclosures for the electronics. Emerging classes of flexible, biointegrated electronic systems demand similar levels of isolation from biofluids but with thin, compliant films that can simultaneously serve as biointerfaces for sensing and/or actuation while in contact with the soft, curved, and moving surfaces of target organs. This paper introduces a solution to this materials challenge that combines (i) ultrathin, pristine layers of silicon dioxide (SiO2) thermally grown on device-grade silicon wafers, and (ii) processing schemes that allow integration of these materials onto flexible electronic platforms. Accelerated lifetime tests suggest robust barrier characteristics on timescales that approach 70 y, in layers that are sufficiently thin (less than 1 µm) to avoid significant compromises in mechanical flexibility or in electrical interface fidelity. Detailed studies of temperature- and thickness-dependent electrical and physical properties reveal the key characteristics. Molecular simulations highlight essential aspects of the chemistry that governs interactions between the SiO2 and surrounding water. Examples of use with passive and active components in high-performance flexible electronic devices suggest broad utility in advanced chronic implants.

A multiscale model for charge inversion in electric double layers.

Charge inversion is a widely observed phenomenon. It is a result of the rich statistical mechanics of the molecular interactions between ions, solvent, and charged surfaces near electric double layers (EDLs). Electrostatic correlations between ions and hydration interactions between ions and water molecules play a dominant role in determining the distribution of ions in EDLs. Due to highly polar nature of water, near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Classical continuum theories fail to accurately describe electrostatic correlations and molecular effects of water in EDLs. In this work, we present an empirical potential based quasi-continuum theory (EQT) to accurately predict the molecular-level properties of aqueous electrolytes. In EQT, we employ rigorous statistical mechanics tools to incorporate interatomic interactions, long-range electrostatics, correlations, and orientation polarization effects at a continuum-level. Explicit consideration of atomic interactions of water molecules is both theoretically and numerically challenging. We develop a systematic coarse-graining approach to coarse-grain interactions of water molecules and electrolyte ions from a high-resolution atomistic scale to the continuum scale. To demonstrate the ability of EQT to incorporate the water orientation polarization, ion hydration, and electrostatic correlations effects, we simulate confined KCl aqueous electrolyte and show that EQT can accurately predict the distribution of ions in a thin EDL and also predict the complex phenomenon of charge inversion.

Integral equation theory based direct and accelerated systematic coarse-graining approaches.

Coarse-grained (CG) molecular dynamics (MD) simulations have become popular for investigating systems on multiple length and time scales ranging from atomistic to mesoscales. In CGMD, several atoms are mapped onto a single CG bead and the effective interactions between CG beads are determined. Iterative coarse-graining methods, such as iterative Boltzmann inversion (IBI), are computationally expensive and can have convergence issues. In this paper, we present a direct and computationally efficient theoretical procedure for coarse-graining based on the Ornstein-Zernike (OZ) and hypernetted chain (HNC) integral equation theory. We demonstrate the OZ-HNC-based CG method by coarse-graining a bulk water system, a water-methanol mixture system, and an electrolyte system. We show that the accuracy of the CG potentials obtained from the OZ-HNC-based coarse-graining is comparable to iterative systematic coarse-graining methods. Furthermore, we show that the CG potentials from OZ-HNC can be used to reduce the number of iterations and hence the computational cost of the iterative systematic coarse-graining approaches, like IBI and relative entropy minimization.

Langevin-Poisson-EQT: A dipolar solvent based quasi-continuum approach for electric double layers.

Water is a highly polar solvent. As a result, electrostatic interactions of interfacial water molecules play a dominant role in determining the distribution of ions in electric double layers (EDLs). Near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Therefore, a detailed description of the structural and dielectric properties of water is important to study EDLs. However, most theoretical models ignore the molecular effects of water and treat water as a background continuum with a uniform dielectric permittivity. Explicit consideration of water polarization and hydration of ions is both theoretically and numerically challenging. In this work, we present an empirical potential-based quasi-continuum theory (EQT) for EDL, which incorporates the polarization and hydration effects of water explicitly. In EQT, water molecules are modeled as Langevin point dipoles and a point dipole based coarse-grained model for water is developed systematically. The space dependence of the dielectric permittivity of water is included in the Poisson equation to compute the electrostatic potential. In addition, to reproduce hydration of ions, ion-water coarse-grained potentials are developed. We demonstrate the EQT framework for EDL by simulating NaCl aqueous electrolyte confined inside slit-like capacitor channels at various ion concentrations and surface charge densities. We show that the ion and water density predictions from EQT agree well with the reference molecular dynamics simulations.

An EQT-based cDFT approach for thermodynamic properties of confined fluid mixtures.

We present an empirical potential-based quasi-continuum theory (EQT) to predict the structure and thermodynamic properties of confined fluid mixtures. The central idea in the EQT is to construct potential energies that integrate important atomistic details into a continuum-based model such as the Nernst-Planck equation. The EQT potentials can be also used to construct the excess free energy functional, which is required for the grand potential in the classical density functional theory (cDFT). In this work, we use the EQT-based grand potential to predict various thermodynamic properties of a confined binary mixture of hydrogen and methane molecules inside graphene slit channels of different widths. We show that the EQT-cDFT predictions for the structure, surface tension, solvation force, and local pressure tensor profiles are in good agreement with the molecular dynamics simulations. Moreover, we study the effect of different bulk compositions and channel widths on the thermodynamic properties. Our results reveal that the composition of methane in the mixture can significantly affect the ordering of molecules and thermodynamic properties under confinement. In addition, we find that graphene is selective to methane molecules.

A multiscale transport model for non-classical nanochannel electroosmosis.

We present a multiscale model describing the electroosmotic flow (EOF) in nanoscale channels involving high surface charge liquid-solid interfaces. The departure of the EOF velocity profiles from classical predictions is explained by the non-classical charge distribution in the confined direction including charge inversion, reduced mobility of interfacial counter-ions, and subsequent enhancement of the local viscosity. The excess component of the local solvent viscosity is modeled by the local application of the Fuoss-Onsager theory and the Hubbard-Onsager electro-hydrodynamic equation based dielectric friction theory. The electroosmotic slip velocity is estimated from the interfacial friction coefficient, which in turn is calculated using a generalized Langevin equation based dynamical framework. The proposed model for local viscosity enhancement and EOF velocity shows good agreement of corresponding physical quantities against relevant molecular dynamics simulation results, including the cases of anomalous transport such as EOF reversal.

A multiscale transport model for Lennard-Jones binary mixtures based on interfacial friction.

We propose a one-dimensional isothermal hydrodynamic transport model for non-reacting binary mixtures in slit shaped nanochannels. The coupled species momentum equations contain viscous dissipation and interspecies friction term of Maxwell-Stefan form. Species partial viscosity variations in the confinement are modeled using the van der Waals one fluid approximation and the local average density method. Species specific macroscopic friction coefficient based Robin boundary conditions are provided to capture the species wall slip effects. The value of this friction coefficient is computed using a species specific generalized Langevin formulation. Gravity driven flow of methane-hydrogen and methane-argon mixtures confined between graphene slit shaped nanochannels are considered as examples. The proposed model yields good quantitative agreement with the velocity profiles obtained from the non-equilibrium molecular dynamics simulations. The mixtures considered are observed to behave as single species pseudo fluid, with the interfacial friction displaying linear dependence on molar composition of the mixture. The results also indicate that the different species have different slip lengths, which remain unchanged with the channel width.

Memory effects in nanoparticle dynamics and transport.

In this work, we use the generalized Langevin equation (GLE) to characterize and understand memory effects in nanoparticle dynamics and transport. Using the GLE formulation, we compute the memory function and investigate its scaling with the mass, shape, and size of the nanoparticle. It is observed that changing the mass of the nanoparticle leads to a rescaling of the memory function with the reduced mass of the system. Further, we show that for different mass nanoparticles it is the initial value of the memory function and not its relaxation time that determines the "memory" or "memoryless" dynamics. The size and the shape of the nanoparticle are found to influence both the functional-form and the initial value of the memory function. For a fixed mass nanoparticle, increasing its size enhances the memory effects. Using GLE simulations we also investigate and highlight the role of memory in nanoparticle dynamics and transport.

Interfacial friction based quasi-continuum hydrodynamical model for nanofluidic transport of water.

In this work, we formulate a one-dimensional isothermal hydrodynamic transport model for water, which is an extension to our recently proposed hydrodynamic model for Lennard-Jones type fluid [R. Bhadauria and N. R. Aluru, J. Chem. Phys. 139, 074109 (2013)]. Viscosity variations in confinement are incorporated by the local average density method. Dirichlet boundary conditions are provided in the form of slip velocity that depends upon the macroscopic interfacial friction coefficient. The value of this friction coefficient is computed using a novel generalized Langevin equation formulation that eliminates the use of equilibrium molecular dynamics simulation. Gravity driven flows of SPC/E water confined between graphene and silicon slit shaped nanochannels are considered as examples for low and high friction cases. The proposed model yields good quantitative agreement with the velocity profiles obtained from non-equilibrium molecular dynamics simulations.

An EQT-based cDFT approach for a confined Lennard-Jones fluid mixture.

Empirical potential-based quasi-continuum theory (EQT) provides a route to incorporate atomistic detail into continuum framework such as the Nernst-Planck equation. EQT can also be used to construct a grand potential functional for classical density functional theory (cDFT). The combination of EQT and cDFT provides a simple and fast approach to predict the inhomogeneous density, potential profiles, and thermodynamic properties of confined fluids. We extend the EQT-cDFT approach to confined fluid mixtures and demonstrate it by simulating a mixture of methane and hydrogen inside slit-like channels of graphene. We show that the EQT-cDFT predictions for the structure of the confined fluid mixture compare well with the molecular dynamics simulation results. In addition, our results show that graphene slit nanopores exhibit a selective adsorption of methane over hydrogen.

An EQT-cDFT approach to determine thermodynamic properties of confined fluids.

We present a continuum-based approach to predict the structure and thermodynamic properties of confined fluids at multiple length-scales, ranging from a few angstroms to macro-meters. The continuum approach is based on the empirical potential-based quasi-continuum theory (EQT) and classical density functional theory (cDFT). EQT is a simple and fast approach to predict inhomogeneous density and potential profiles of confined fluids. We use EQT potentials to construct a grand potential functional for cDFT. The EQT-cDFT-based grand potential can be used to predict various thermodynamic properties of confined fluids. In this work, we demonstrate the EQT-cDFT approach by simulating Lennard-Jones fluids, namely, methane and argon, confined inside slit-like channels of graphene. We show that the EQT-cDFT can accurately predict the structure and thermodynamic properties, such as density profiles, adsorption, local pressure tensor, surface tension, and solvation force, of confined fluids as compared to the molecular dynamics simulation results.

Effect of intermolecular force on the static/dynamic behaviour of M/NEM devices.

Advances made in the fabrication of micro/nano-electromechanical (M/NEM) devices over the last ten years necessitate the understanding of the attractive force that arises from quantum fluctuations (generally referred to as Casimir effects) [Casimir H B G 1948 Proc. K. Ned. Akad. Wet. 51 793]. The fundamental mechanisms underlying quantum fluctuations have been actively investigated through various theoretical and experimental approaches. However, the effect of the force on M/NEM devices has not been fully understood yet, especially in the transition region involving gaps ranging from 10 nm to 1 µm, due to the complexity of the force. Here, we numerically calculate the Casimir effects in M/NEM devices by using the Lifshitz formula, the general expression for the Casimir effects [Lifshitz E 1956 Sov. Phys. JETP 2 73]. Since the Casimir effects are highly dependent on the permittivity of the materials, the Kramer-Kronig relation [Landau L D, Lifshitz E M and Pitaevskii L P 1984 Electrodynamics of Continuous Media (New York: Pergamon Press)] and the optical data for metals and dielectrics are used in order to obtain the permittivity. Several simplified models for the permittivity of the materials, such as the Drude and Lorentz models [Jackson J D 1975 Classical Electrodynamics (New York: Wiley)], are also used to extrapolate the optical data. Important characteristic values of M/NEM devices, such as the pull-in voltage, pull-in gap, detachment length, etc, are calculated for devices operating in the transition region. Our results show that accurate predictions for the pull-in behaviour are possible when the Lifshitz formula is used instead of the idealized expressions for Casimir effects. We expand this study into the dynamics of M/NEM devices, so that the time and frequency response of M/NEM devices with Casimir effects can be explored.